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A novel multiobjective evolutionary algorithm based on regression analysis.

Song Z, Wang M, Dai G, Vasile M - ScientificWorldJournal (2015)

Bottom Line: The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages.At the same time, MMEA-RA has higher efficiency than the other two algorithms.A few shortcomings of MMEA-RA have also been identified and discussed in this paper.

View Article: PubMed Central - PubMed

Affiliation: School of Computer, China University of Geosciences, Wuhan 430074, China.

ABSTRACT
As is known, the Pareto set of a continuous multiobjective optimization problem with m objective functions is a piecewise continuous (m - 1)-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multiobjective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multiobjective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multiobjective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m - 1)-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based on the nondominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithms. A few shortcomings of MMEA-RA have also been identified and discussed in this paper.

No MeSH data available.


Related in: MedlinePlus

The final nondominated solutions and fronts found by RE-MEDA. (a) The result with the lowest γ-metric and (b) all the 10 fronts in 10 runs.
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fig9: The final nondominated solutions and fronts found by RE-MEDA. (a) The result with the lowest γ-metric and (b) all the 10 fronts in 10 runs.

Mentions: The final nondominated solutions and fronts obtained by RM-MEDA on the test case are shown in Figure 9. Similarly, Figure 9(a) is the result with the lowest γ-metric obtained in 10 runs while Figure 9(b) gives all the 10 fronts in 10 runs. Similar to Figure 8, the nondominated solution(s) in Figures 9(a) and 9(b) are marked with red. The Pareto fronts are marked with blue. The Pareto fronts are given in Figures 9(a) and 9(b) only for comparing the quality of the nondominated solutions. It can be seen that the nondominated front with the lowest γ-metric is very consistent with the Pareto front although there are some differences between them. In particular, it should be noted that all results in 10 runs from RM-MEDA match the Pareto front better than MMEA-RA. But it also should be noted that there is an isolated point in the nondominated solutions for all 10 runs in Figure 9(b), maybe because RM-MEDA falls into a local minimum and could not jump out.


A novel multiobjective evolutionary algorithm based on regression analysis.

Song Z, Wang M, Dai G, Vasile M - ScientificWorldJournal (2015)

The final nondominated solutions and fronts found by RE-MEDA. (a) The result with the lowest γ-metric and (b) all the 10 fronts in 10 runs.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4385692&req=5

fig9: The final nondominated solutions and fronts found by RE-MEDA. (a) The result with the lowest γ-metric and (b) all the 10 fronts in 10 runs.
Mentions: The final nondominated solutions and fronts obtained by RM-MEDA on the test case are shown in Figure 9. Similarly, Figure 9(a) is the result with the lowest γ-metric obtained in 10 runs while Figure 9(b) gives all the 10 fronts in 10 runs. Similar to Figure 8, the nondominated solution(s) in Figures 9(a) and 9(b) are marked with red. The Pareto fronts are marked with blue. The Pareto fronts are given in Figures 9(a) and 9(b) only for comparing the quality of the nondominated solutions. It can be seen that the nondominated front with the lowest γ-metric is very consistent with the Pareto front although there are some differences between them. In particular, it should be noted that all results in 10 runs from RM-MEDA match the Pareto front better than MMEA-RA. But it also should be noted that there is an isolated point in the nondominated solutions for all 10 runs in Figure 9(b), maybe because RM-MEDA falls into a local minimum and could not jump out.

Bottom Line: The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages.At the same time, MMEA-RA has higher efficiency than the other two algorithms.A few shortcomings of MMEA-RA have also been identified and discussed in this paper.

View Article: PubMed Central - PubMed

Affiliation: School of Computer, China University of Geosciences, Wuhan 430074, China.

ABSTRACT
As is known, the Pareto set of a continuous multiobjective optimization problem with m objective functions is a piecewise continuous (m - 1)-dimensional manifold in the decision space under some mild conditions. However, how to utilize the regularity to design multiobjective optimization algorithms has become the research focus. In this paper, based on this regularity, a model-based multiobjective evolutionary algorithm with regression analysis (MMEA-RA) is put forward to solve continuous multiobjective optimization problems with variable linkages. In the algorithm, the optimization problem is modelled as a promising area in the decision space by a probability distribution, and the centroid of the probability distribution is (m - 1)-dimensional piecewise continuous manifold. The least squares method is used to construct such a model. A selection strategy based on the nondominated sorting is used to choose the individuals to the next generation. The new algorithm is tested and compared with NSGA-II and RM-MEDA. The result shows that MMEA-RA outperforms RM-MEDA and NSGA-II on the test instances with variable linkages. At the same time, MMEA-RA has higher efficiency than the other two algorithms. A few shortcomings of MMEA-RA have also been identified and discussed in this paper.

No MeSH data available.


Related in: MedlinePlus